Using Cofactors of elements of second row, evaluate.

The given determinant is.

We have:

M₂₁ =

∴A₂₁ = cofactor of a₂₁ = (−1)²⁺¹ M₂₁ = 7

M₂₂ =

∴A₂₂ = cofactor of a₂₂ = (−1)²⁺² M₂₂ = 7

M₂₃ =

∴A₂₃ = cofactor of a₂₃ = (−1)²⁺³ M₂₃ = −7

We know that Δ is equal to the sum of the product of the elements of the second row with their corresponding cofactors.

∴Δ = a₂₁A₂₁ + a₂₂A₂₂ + a₂₃A₂₃ = 2(7) + 0(7) + 1(−7) = 14 − 7 = 7